Consider an economy with two states of nature and one time period. An option pays $3 in state 1 and $0 in state 2, and is being traded for the price of $1. A forward contract pays $3 in state 1 and -$2 in state 2. Using this information, compute the risk-free rate and the risk-neutral probabilities for each state of nature.
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Consider an economy with two states of nature and one time period. An option pays $3 in state 1 and $0 in state 2, and is being traded for the price of $1. A forward contract pays $3 in state 1 and -$2 in state 2. Using this information, compute the risk-free rate and the risk-neutral probabilities for each state of nature.
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- A manufacturer produces a toy sold during the summer season at a unit production cost of $5. The manufacturer sells the toy to a retailer, who then sells the product for $35 to the end customer. The manufacturer and retailer have agreed upon a revenue sharing contract that coordinates the supply chain and optimizes the expected profit of the entire supply chain (i.e., the retailer and the manufacturer), which is expected to be $4,000 over the summer selling season. If the wholesale price of the revenue sharing contract is $2, what is the manufacturer’s expected profit? PLEASE SHOW CALCULATIONSAn investor plans to put $50,000 in one of four investments. The return on each investment depends on whether next year's economy is strong or weak. The following table summarizes the possible payoffs, in dollars, for the four investments. Certificate of deposit Office complex Land speculation Technical school Next year's economy Strong 7,000 15,000 32,500 6,000 Weak 7,000 4,500 - 17,000 12,000 Let V, W, X, and Y denote the payoffs for the certificate of deposit, office complex, land speculation, and technical school, respectively. Then V, W, X, and Y are random variables. Assume that next year's economy has a 30% chance of being strong and a 70% chance of being weak. a. Find the probability distribution of each random variable V, W, X, and Y. What is the probability distribution for V? V 7,000 P(V=v)A company is considering a project which has three options. The payoffs are shown in the body of the table. In this instance, the payoffs are in terms of present values, which represent equivalent current dollar values of expected future income less costs. This is a convenient measure because it places all alternatives on a comparable basis. If a small facility is built, the payoff will be the same for all three possible states of nature. For a medium facility, low demand will have a present value of $7 million, whereas both moderate and high demand will have present values of $12 million. A large facility will have a loss of $4 million if demand is low, a present value of $2 million if demand is moderate, and a present value of $16 million if demand is high. The payoff table depicting revenues and is shown in the following table. payoffs (PV in millions) states of nature Low Option Moderate high Small 10 10 10 Medium 7 12 12 Large -4 2 16 (a) Which alternative should the manager…
- The table here shows the no-arbitrage prices of securities A and B that we calculated.Cash Flow in One YearSecurity Market Price Today Weak Economy Strong EconomySecurity A 231 0 600Security B 346 600 0a. What are the payoffs of a portfolio of one share of security A and one share of security B?b. What is the market price of this portfolio? What expected return will you earn from holdingthis portfolio?A company is considering a project which has three options. The payoffs are shown in the body of the table. In this instance, the payoffs are in terms of present values, which represent equivalent current dollar values of expected future income less costs. This is a convenient measure because it places all alternatives on a comparable basis. If a small facility is built, the payoff will be the same for all three possible states of nature. For a medium facility, low demand will have a present value of $7 million,whereas both moderate and high demand will have present values of $12 million. A large facility will have a loss of $4 million if demand is low, a present value of $2 million if demand is moderate, and a present value of $16 million if demand is high.The payoff table depicting revenues and is shown in the following table. (a) Which alternative should the manager choose under the maximax criterion? (b) Which option should the manager choose under the maximin criterion? (c) Which…